Babies & Insurance

Does anyone know how insurance works for baby/delivery. Currently I’m on my step moms insurance (I’m 25) and my fiancé has insurance through the military but just for himself. He works another full time job that offers insurance but he gets an extra amount of money for not taking it. I don’t know how it works with delivering... is it my current insurance that is billed for me delivering and then separate billing for the baby? My hope was once I go back to work (approx 2 months after giving birth) to add the baby to insurance so we are still getting that extra income until then. Sorry if this is a stupid question/thought but first time mom & I am not sure how this all works... thank you!